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The list of words from that trivial alphabet is certainly generatable via a function though.
by davrosthedalek 9y ago
The list of words from that trivial alphabet is certainly generatable via a function though.
- dvt 9y agoTrue, but the generation will never terminate (as the list is countably infinite). Your next argument might be "oh I just need to generate T until I hit f_i" -- which is true, but then I can introduce another function f_i_i which will bungle up your system again :) But this gets into the Second Incompleteness Theorem.
- davrosthedalek 9y agoThe point is that you cannot find an alphabet to generate all terminating programs. The infinite nature of T is really not the problem.